MMR- Mode, Median, and RangeBy: Natalya Spatarel and Stephanie Renneberg
6th grade Common Core State Standard: Statistics and Probability Summarize and describe distributions 6.SP.5. Summarize numerical data sets in relation to their context, such as by: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
Student learning objectives: Students will be able to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. Students will be able to recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. Students will be able to evaluate how the median measures the center in the sense that it is roughly the middle value. Students will be able to evaluate how the mean measures the center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students will be able to recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability.
regular playing card deck with Jack, Queen, King and Jokers removed
Directions:
Each player is given a game board. Place the MMR cards in the middle, equal distance away from all players.
The dealer is the oldest player and he/she deals 5 cards from the deck to every player. The players cannot look at their cards.
On the count of three, all players will look at their cards. Once a player has found the mode, median and range of their data (card set) they place these cards on the board in the appropriate spots. Once any player has a complete board, they must grab a MMR card from the middle. There are not enough letters, one player will be out.
Rules!
If the player has more than one mode they may choose either one
Only place one of the mode cards on the game board in the mode section
Ace is low- Represented as 1
You will be left with a remaining card that does not go on your board
If you make any changes to your board you must put the MMR card back in the center to make your changes. If you do not you are automatically out.
IF YOU ARE THE LAST PLAYER WITHOUT A MMR CARD; you have the chance to steal an MMR card. You must double check the other player’s game boards. If a player has incorrect cards on their board you may steal their MMR card.
Repeat steps 1-3, taking away a MMR card after each round. There should always be one less card then the number of players. The last player with a MMR card wins!
Summary game questions: 1. When would you need to find the median, mode, or range in a real-world problem? 2. Why is this information important in any set of data? 3. Give your definition of median, mode, and range? 4. How would you find the average, or mean, of a set of data? a. For extension lesson 5. Is the difference between the average and the actual data points significant or relevant? If so, why and does the difference have a name?
Extension: The optional substitution or challenge for stealing an MMR card from a winning player could be to calculate the mean of the data set and the highest mean steals the card. This will allow students to become more familiar with mean, or average, while still enjoying the competitive nature of the game.
MMR- Mode, Median, and RangeBy: Natalya Spatarel and Stephanie Renneberg
6th grade
Common Core State Standard:
Statistics and Probability
Summarize and describe distributions
6.SP.5. Summarize numerical data sets in relation to their context, such as by:
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
Student learning objectives:
Students will be able to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.
Students will be able to recognize that a data distribution may not have a definite center and that different ways to measure center yield different values.
Students will be able to evaluate how the median measures the center in the sense that it is roughly the middle value.
Students will be able to evaluate how the mean measures the center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point.
Students will be able to recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability.
Materials:
Directions:
- Each player is given a game board. Place the MMR cards in the middle, equal distance away from all players.
- The dealer is the oldest player and he/she deals 5 cards from the deck to every player. The players cannot look at their cards.
- On the count of three, all players will look at their cards. Once a player has found the mode, median and range of their data (card set) they place these cards on the board in the appropriate spots. Once any player has a complete board, they must grab a MMR card from the middle. There are not enough letters, one player will be out.
Rules!Summary game questions:
1. When would you need to find the median, mode, or range in a real-world problem?
2. Why is this information important in any set of data?
3. Give your definition of median, mode, and range?
4. How would you find the average, or mean, of a set of data?
a. For extension lesson
5. Is the difference between the average and the actual data points significant or relevant? If so, why and does the difference have a name?
Extension:
The optional substitution or challenge for stealing an MMR card from a winning player could be to calculate the mean of the data set and the highest mean steals the card. This will allow students to become more familiar with mean, or average, while still enjoying the competitive nature of the game.